A number of encryption methods and cryptographic systems (cryptosystems) are currently used in various fields. For example, there are symmetric cryptosystems and asymmetric cryptosystems. The symmetric cryptography, which is also referred to as secret-key cryptography, uses a single key (secret key) to encrypt and decrypt information. Asymmetric cryptography, which is also referred to as public-key cryptography, uses a pair of keys: one (public key) to encrypt data, and the other (private key) to decrypt it. Currently available encryption algorithms include, for example, Data Encryption Standard (DES) which is a symmetric algorithm employing a block cipher with a single 56-bit key, triple DES which is a secure form of DES using a 168-bit key, International Data Encryption Algorithm (IDEA) which is a block-mode secret-key encryption algorithm using a 128-bit key, RC4 which is a widely-used symmetric key algorithm, the Advanced Encryption Standard (AES) which provides stronger encryption scheme with alternative three key lengths of 128 bits, 192 bits, or 256 bits, and the like.
Many companies employ a symmetric cryptosystem for their secure communications, using a predetermined encryption algorithm with the fixed secret-key such as the triple DES or AES. Due to the continuous evolution of computer-based technology, security methods that have seemed unbreakable are becoming inadequate, for example, the 56-bit key size of DES is no longer considered secure against brute force attacks. Using the same encryption algorithm and the same secret-key for communication over long time may increase the risk of brute force attacks on the cryptosystem. However, replacing encryption algorithm and/or the secret-key in a once-implemented cryptosystem is typically very costly, since it requires some form of secure key exchange, in person, by courier, and the like, among all of the entities using the cryptosystem, and any change in the algorithm or secret key must also be synchronized among the entities. A fixed algorithm/key cryptosystem also lacks compatibility with other cryptosystems utilizing a different encryption algorithm and/or a different secret key.
Accordingly, it would be desirable to provide a cryptosystem which realizes secure communications and transactions which is less vulnerable to brute force and other attacks and also has high flexibility and compatibility.